Polynesian Journal of Mathematics

Volume 4, Issue 9
Special volume AJAX in honor of René Schoof

On the ℓ-part of Iwasawa modules in ℤ_p-extensions

Andrea Bandini and Ignazio Longhi

Abstract:

We give a short summary of the main algebraic results of [Bandini & Longhi, 2026] on ${\mathbb{Z}}_{\ell }\left[\right[\mathrm{\Gamma }\left]\right]$-modules (with $\mathrm{\Gamma }$ an abelian pro-$p$-group and $\ell \ne p$ two different primes) and use them to provide an algebraic interpretation of known results on $\ell$-parts of Iwasawa modules (such as class groups and duals of Selmer groups) in ${\mathbb{Z}}_p$-extensions, which were previously obtained via $\ell$-adic interpolation and/or special values of $L$-functions. This algebraic approach leads to natural questions which could be the starting point for future research.

Citation:

Andrea Bandini and Ignazio Longhi. On the ℓ-part of Iwasawa modules in ℤ_p-extensions. Polynesian Journal of Mathematics, Volume 4, Issue 9, Pages 1–29. (Sept. 2026) DOI: 10.69763/polyjmath.4.9

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Milestones:

Received 18 Feb 2026
Revised 4 May 2026
Accepted 17 May 2026
Published 28 Sep 2026
Communicated by Samuele Anni

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